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notsponge [240]

3 years ago

12

1) A car is traveling down the interstate at 37.1 m/s. The driver sees a cop and quickly slows down. If the driver slows to 29.8

m/s in 3 seconds, what is the acceleration of the car?
2) While cleaning you lift an 87.3 N box up to a shelf that is 2.04 m above the ground. How much work was done on the box?

3) A child runs up the stairs and does 1250 J of work. If the child generates 267 W of power how long did it take for the child to run up the stairs?

1 answer:

dlinn [17]3 years ago

3 0

Explanation:

1. Acceleration is the change in velocity over time.

a = Δv / Δt

a = (29.8 m/s − 37.1 m/s) / 3 s

a = -2.43 m/s²

2. Work equals force times distance.

W = Fd

W = (87.3 N) (2.04 m)

W = 178 J

3. Power is work per time.

P = W / t

267 W = 1250 J / t

t = 4.68 s

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Explanation:

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At a depth of 1030 m in Lake Baikal (a fresh water lake in Siberia), the pressure has increased by 100 atmospheres (to about 107

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Answer:

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Explanation:

The bulk modulus is represented by the following differential equation:

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Where:

$K$ - Bulk module, measured in pascals.

$V$ - Sample volume, measured in cubic meters.

$P$ - Local pressure, measured in pascals.

Now, let suppose that bulk remains constant, so that differential equation can be reduced into a first-order linear non-homogeneous differential equation with separable variables:

$-\frac{K \,dV}{V} = dP$

This resultant expression is solved by definite integration and algebraic handling:

$-K\int\limits^{V_{f}}_{V_{o}} {\frac{dV}{V} } = \int\limits^{P_{f}}_{P_{o}}\, dP$

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$\ln \left| \frac{V_{f}}{V_{o}} \right| = \frac{P_{o}-P_{f}}{K}$

$\frac{V_{f}}{V_{o}} = e^{\frac{P_{o}-P_{f}}{K} }$

The final volume is predicted by:

$V_{f} = V_{o}\cdot e^{\frac{P_{o}-P_{f}}{K} }$

If $V_{o} = 1\,m^{3}$ , $P_{o} - P_{f} = -10132500\,Pa$ and $K = 2.3\times 10^{9}\,Pa$ , then:

$V_{f} = (1\,m^{3}) \cdot e^{\frac{-10.1325\times 10^{6}\,Pa}{2.3 \times 10^{9}\,Pa} }$

$V_{f} \approx 0.996\,m^{3}$

Change in volume due to increasure on pressure is:

$\Delta V = V_{o} - V_{f}$

$\Delta V = 1\,m^{3} - 0.996\,m^{3}$

$\Delta V = 0.004\,m^{3}$

A volume of a cubic meter of water from the surface of the lake has been compressed in 0.004 cubic meters.

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3 years ago